当一个小儿子在哭泣而妈妈为了让他睡觉就拿他上来而用胳膊轻轻的动他,这用汉语叫什么？
When a young child is crying and the mother in order to make him sleep takes him up and gently move him with her arms, what do you call that in Chinese?
PS If there is anything to improve in the Chinese version, please tell me. I know the title should be informative but to make it more informative I would practically have had to put the question in the title, or cause ambiguities with English translations like "rock".
The question is not very clear to me. It seems that the request is for a word which unambiguously indicates that the mother is holding the baby in her arms and rocking it. I don't think there is such a word in Chinese. My first choice for the action of rocking a baby would be 搖, but like English 'rock' this is ambiguous as to how the rocking is done. Here are English and Chinese examples:
In both the English and Chinese examples, the baby could be in the mother's arms, or in a cradle. I think the only way to clarify this in Chinese is to add a descriptive phrase. One possibility is to add the word 抱; this is the standard word for holding something in one's arms. If you use this, you will need to think a bit about how babies are held. If you have the baby in front with its head resting against your chest, this is called 抱在懷裡. If you hold the baby with its head resting on your shoulder and one arm under its bottom, this is probably just 抱, so for example:
If you are trying to fit words to a song, try verb reduplication. 抱啊抱, 搖啊搖, etc. This how people actually talk to babies when they are trying to get them to sleep, or anyway this is how I did it.
One thing to be careful about: English 'rock' refers to a semi-circular motion; Chinese 搖 is not limited to this, and sometimes just means 'to shake'. However, in English, to shake a baby is usually taken as crossing a very dangerous line, and might even be taken to mean that one is unfit to care for a child. If you ever interpret in a court case involving something like this, be careful!! You cannot take the word 搖 to automatically mean 'shake vigorously'! You must explain to the court participants how the Chinese works and specifically ask in Chinese how the child was held and what degree of force was used; do not unfairly prejudice the judge or jury against the Chinese speaker.
My own feeling is that Chinese takes as conventional the sense that 搖 is appropriate for the baby. Sometimes inexperienced children do it with too much enthusiasm, and the usual correction is 搖輕一點!
This translation of 'Rock a bye baby' from 百度 gives 'the cradle will rock' as '摇篮就会摇摆'
宝宝的摇篮在树枝上，当风吹起时，摇篮就会摇摆。当树枝断裂，摇篮就和宝宝都掉下来了抓住宝宝和摇篮叻。
摇 or 摇摆 should convey the message of 'move something back and forth'. I think it is more Chinese to say '抱着宝宝哄‘
As to why the English put their babies in treetops to sleep, your guess is as good as mine!
Edit: Did I get the question wrong? Do you want to formulate the question properly?
当一个小儿子在哭泣而妈妈为了让他睡觉就拿他上来而用胳膊轻轻的动他,
That could be:
妈妈把哭闹的孩子抱在怀里轻轻的摇晃,
哄
Here's an example from 21century dictionary
It took the mother half an hour to get the baby off to sleep.
母亲花了半个小时才把婴儿哄睡着了。
Here the full phrase is 哄睡着.
